Question: Express this product in scientific notation: $(4.60\times 10^{-3})\times (4.00\times 10^{3})$
Answer: Start by collecting like terms together. $= (4.60\times 4.00) \times (10^{-3}\times 10^{3})$ When multiplying exponents with the same base, add the powers together. $= 18.4 \times 10^{-3\,+\,3}$ $= 18.4 \times 10^{0}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $18.4$ is the same as $1.840 \times 10$ $ = {1.840 \times 10} \times 10^{0} $ $= 1.840\times 10^{1}$